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Journal of Combinatorial Optimization

, Volume 27, Issue 2, pp 256–270 | Cite as

A study of search algorithms’ optimization speed

  • Andrea Valsecchi
  • Leonardo Vanneschi
  • Giancarlo Mauri
Article

Abstract

Search algorithms are often compared by the optimization speed achieved on some sets of cost functions. Here some properties of algorithms’ optimization speed are introduced and discussed. In particular, we show that determining whether a set of cost functions F admits a search algorithm having given optimization speed is an NP-complete problem. Further, we derive an explicit formula to calculate the best achievable optimization speed when F is closed under permutation. Finally, we show that the optimization speed achieved by some well-know optimization techniques can be much worse than the best theoretical value, at least on some sets of optimization benchmarks.

Keywords

Optimization problems Search algorithms Optimization speed 

References

  1. Aarts E, Korst J (1989) Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing. Wiley, New York MATHGoogle Scholar
  2. Altenberg L (1997) Nk fitness landscapes. In: Back T, et al. (eds) Handbook of evolutionary computation. IOP Publishing Ltd and Oxford University Press, Bristol, pp B2.7:5–B2.7:10 Google Scholar
  3. Deb K, Goldberg DE (1993) Analyzing deception in trap functions. In: Whitley D (ed) Foundations of genetic algorithms, vol 2. Morgan Kaufmann, San Mateo, pp 93–108 Google Scholar
  4. English TM (2004) On the structure of sequential search: beyond “no free lunch”. In: Gottlieb J, Raidl GR (eds) EvoCOP. Lecture notes in computer science, vol 3004. Springer, Berlin, pp 95–103 Google Scholar
  5. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading MATHGoogle Scholar
  6. Häggström O (2006) Intelligent design and the nfl theorems. Biol Philos 22(2):217–230 CrossRefGoogle Scholar
  7. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor Google Scholar
  8. Hyafil L, Rivest RL (1976) Constructing optimal binary decision trees is NP-complete. Inf Process Lett 5(1):15–17 CrossRefMATHMathSciNetGoogle Scholar
  9. Igel C, Toussaint M (2004) A no-free-lunch theorem for non-uniform distributions of target functions. J Math Model Algorithms 3(4):313–322 CrossRefMATHMathSciNetGoogle Scholar
  10. Jackson K, Kreinin A, Zhang W (2009) Randomization in the first hitting time problem. Stat Probab Lett 79(23):2422–2428. doi: 10.1016/j.spl.2009.08.016 CrossRefMATHMathSciNetGoogle Scholar
  11. Radcliffe N, Surry PD (1995) Fundamental limitations on search algorithms: evolutionary computing in perspective. Lecture notes in computer science, vol 1000. Springer, Berlin, pp 275–291 Google Scholar
  12. Rowe JE, Vose MD, Wright AH (2009) Reinterpreting no free lunch. Evol Comput 17:117–129. DOI http://dx.doi.org/10.1162/evco.2009.17.1.117. URL http://dx.doi.org/10.1162/evco.2009.17.1.117 CrossRefGoogle Scholar
  13. Schumacher C, Vose MD, Whitley LD (2001) The no free lunch and problem description length. In: Spector L, Goodman ED, Wu A, Langdon WB, Voigt HM, Gen M, Sen S, Dorigo M, Pezeshk S, Garzon MH, Burke E (eds) Proceedings of the genetic and evolutionary computation conference (GECCO-2001). Morgan Kaufmann, San Francisco, pp 565–570. URL cite-seer.ist.psu.edu/schumacher01no.html Google Scholar
  14. Valsecchi A, Vanneschi L (2008) A study of some implications of the no free lunch theorem. In: Gi- acobini M, et al. (eds) International workshop on theoretical aspects in artificial evolution, EvoTheory 2008. Proceedings of applications of evolutionary computing, EvoWorkshops 2008. Lecture notes in computer science, vol 4974. Springer, Berlin, pp 633–642 Google Scholar
  15. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82. URL citeseer.ist.psu.edu/wolpert96no.html CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Andrea Valsecchi
    • 1
  • Leonardo Vanneschi
    • 2
    • 3
  • Giancarlo Mauri
    • 2
  1. 1.European Centre for Soft ComputingMieresSpain
  2. 2.DISCoUniversità di Milano-BicoccaMilanItaly
  3. 3.ISEGIUniversidade Nova de LisboaLisbonPortugal

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